TY - JOUR

T1 - Continuous time finite state mean field games

AU - Gomes, Diogo A.

AU - Mohr, Joana

AU - Souza, Rafael Rigão

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: D. Gomes was partially supported by CAMGSD-LARSys through FCT-Portugal and by grants PTDC/MAT-CAL/0749/2012, UTA-CMU/MAT/0007/2009 PTDC/MAT/114397/2009, UTAustin-MAT/0057/2008, and by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. R.R.S. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. J.M. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09.

PY - 2013/4/23

Y1 - 2013/4/23

N2 - In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.

AB - In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.

UR - http://hdl.handle.net/10754/562726

UR - http://link.springer.com/10.1007/s00245-013-9202-8

UR - http://www.scopus.com/inward/record.url?scp=84880206151&partnerID=8YFLogxK

U2 - 10.1007/s00245-013-9202-8

DO - 10.1007/s00245-013-9202-8

M3 - Article

VL - 68

SP - 99

EP - 143

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

SN - 0095-4616

IS - 1

ER -